The MVM operates on networks represented in a hidden metric space described by the \(\mathbb {S}^1\)  geometric network model [1]}. In this space, distances between nodes determine their likelihood to form connections. The \(\mathbb {S}^1\)  model provides every node \(i\)  with a popularity-similarity pair of coordinates \((\kappa _i, \theta _i)\) , where \(\kappa _i\)  is the node's hidden degree (with expected value proportional to the observed degree \(k_i\) ), and \(\theta _i\)  is its similarity coordinate designating an angular position in a circle. Importantly, the more similar two nodes are, the shorter is their angular separation \(\Delta \theta _{ij}=\mathrm {min}(|\theta _i -\theta _j|, 2\pi - |\theta _i -\theta _j|)\)  and the higher the likelihood that they are connected.
